# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/11) | Q#2

Question

Solve the equation  for .

Solution

We are given;

We have the trigonometric identity;

From this identity we can have;

Substituting in given equation;

Let ;

Now we have two options.

Since;

Using calculator we can find the values of .

 NOT POSSIBLE

We utilize the periodic property of   to find other solutions (roots) of :

 Symmetry Property

Hence;

For ;

Therefore, we have two solutions (roots) of the equation;

To find all the solutions (roots) over the interval , we utilize the periodic property of         for both these values of .

 Periodic Property or

Therefore;

 For For

For;

Hence all the solutions (roots) of the equation  for  are;